{
  "id": "1810.02014",
  "version": "v1",
  "published": "2018-10-04T01:01:23.000Z",
  "updated": "2018-10-04T01:01:23.000Z",
  "title": "Bounds on the multiplicity of the Hecke eigenvalues",
  "authors": [
    "Naser T. Sardari"
  ],
  "comment": "Comments are always very welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Fix an integer $N$ and a prime $p\\nmid N$ where $p\\geq 5$. We show that the number of newforms $f$ (up to a scalar multiple) of level $N$ and even weight $k$ such that $\\mathcal{T}_p(f)=0$ is bounded independently of $k$, where $\\mathcal{T}_p(f)$ is the Hecke operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-04T01:01:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke eigenvalues",
      "multiplicity",
      "scalar multiple",
      "hecke operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}